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Story Discrete event simulation Simulation time != real time Key ideas: A Queue A Queue is a queue, no matter how implemented. Different kinds of random Straightening time Inserting it into the right place Sorting it afterwards Building a discrete event simulation Graphics as the representation, not the real thing: The Model and the View

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Imagine the simulation… There are three Trucks that bring product from the Factory. On average, they take 3 days to arrive. Each truck brings somewhere between 10 and 20 products—all equally likely. We’ve got five Distributors who pick up product from the Factory with orders. Usually they want from 5 to 25 products, all equally likely. It takes the Distributors an average of 2 days to get back to the market, and an average of 5 days to deliver the products. Question we might wonder: How much product gets sold like this?

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Don’t use a Continuous Simulation We don’t want to wait that number of days in real time. We don’t even care about every day. There will certainly be timesteps (days) when nothing happens of interest. We’re dealing with different probability distributions. Some uniform, some normally distributed. Things can get out of synch A Truck may go back to the factory and get more product before a Distributor gets back. A Distributor may have to wait for multiple trucks to fulfill orders (and other Distributors might end up waiting in line)

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We use a Discrete Event Simulation We don’t simulate every moment continuously. We simulate discrete events.

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What’s the difference? No time loop In a discrete event simulation: There is no time loop. There are events that are scheduled. At each run step, the next scheduled event with the lowest time gets processed. The current time is then that time, the time that that event is supposed to occur. Key: We have to keep the list of scheduled events sorted (in order)

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What’s the difference? Agents don’t act() In a discrete event simulations, agents don’t act(). Instead, they wait for events to occur. They schedule new events to correspond to the next thing that they’re going to do. Key: Events get scheduled according to different probabilities.

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What’s the difference? Agents get blocked Agents can’t do everything that they want to do. If they want product (for example) and there isn’t any, they get blocked. They can’t schedule any new events until they get unblocked. Many agents may get blocked awaiting the same resource. More than one Distributor may be awaiting arrival of Trucks Key: We have to keep track of the Distributors waiting in line (in the queue)

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Key Ideas A Queue A Queue is a queue, no matter how implemented. Different kinds of random Straightening time Inserting it into the right place Sorting it afterwards

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Key idea #1: Introducing a Queue First-In-First-Out List First person in line is first person served I got here first! I got here second! I got here third! This is the front or head of the queue This is the tail of the queue

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First-in-First-out New items only get added to the tail. Never in the middle Items only get removed from the head. I got here first! I got here second! I got here third! This is the front or head of the queue This is the tail of the queue

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As items leave, the head shifts I got here first! AND NOW I’M UP! I got here second! I got here third! Now, this is the front or head of the queue This is the tail of the queue Served!

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As new items come in, the tail shifts I got here second! I got here third! Now, this is the front or head of the queue Now, this is the tail of the queue I got here fourth!

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What can we do with queues? push(anObject): Tack a new object onto the tail of the queue pop(): Pull the end (head) object off the queue. peek(): Get the head of the queue, but don’t remove it from the queue. size(): Return the size of the queue

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Queue methods /// Methods /** Push an object onto the Queue */ public void push(Object element){ elements.addFirst(element); } /** Peek at, but don't remove, top of queue */ public Object peek(){ return elements.getLast();} /** Pop an object from the Queue */ public Object pop(){ Object toReturn = this.peek(); elements.removeLast(); return toReturn; } /** Return the size of a queue */ public int size() { return elements.size();} We’re using a linked list to implement the Queue. The front of the LinkedList is the tail. The last of the LinkedList is the head.

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A queue is a queue, no matter what lies beneath. Our description of the queue minus the implementation is an example of an abstract data type (ADT). An abstract type is a description of the methods that a data structure knows and what the methods do. We can actually write programs that use the abstract data type without specifying the implementation. There are actually many implementations that will work for the given ADT. Some are better than others.

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Same methods, same behavior Welcome to DrJava. > Queue2 line = new Queue2(); > line.push("Mary") > line.push("Kim") > line.push("Ron") > line.peek() "Mary" > line.pop() "Mary" > line.peek() "Kim" > line.size() 2 > line.pop() "Kim" > line.pop() "Ron" But can only handle up to 20 elements in the queue! Less if pushing and popping. Could shift elements to always allow 20. Not as good an implementation as the linked list implementation. (But uses less memory.)

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Key idea #2: Different kinds of random We’ve been dealing with uniform random distributions up until now, but those are the least likely random distribution in real life. How can we generate some other distributions, including some that are more realistic?

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How do we shift the distribution where we want it? // Fill it with 500 numbers with a mean of 5.0 and a //larger spread, normally distributed for (int i=0; i < 500; i++){ try{ output.write("\t"+((range * rng.nextGaussian())+mean)); output.newLine(); } catch (Exception ex) { System.out.println("Couldn't write the data!"); System.out.println(ex.getMessage()); } Multiply the random nextGaussian() by the range you want, then add the mean to shift it where you want it.

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Key idea #3: Straightening Time Straightening time Inserting it into the right place Sorting it afterwards We’ll actually do these in reverse order: We’ll add a new event, then sort it. Then we’ll insert it into the right place.

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Implementing an EventQueue import java.util.*; /** * EventQueue * It's called an event "queue," but it's not really. * Instead, it's a list (could be an array, could be a linked list) * that always keeps its elements in time sorted order. * When you get the nextEvent, you KNOW that it's the one * with the lowest time in the EventQueue **/ public class EventQueue { private LinkedList elements; /// Constructor public EventQueue(){ elements = new LinkedList(); }

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Two options for add() /** * Add the event. * The Queue MUST remain in order, from lowest time to highest. **/ public void add(SimEvent myEvent){ // Option one: Add then sort elements.add(myEvent); this.sort(); //Option two: Insert into order //this.insertInOrder(myEvent); }

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There are lots of sorts! Lots of ways to keep things in order. Some are faster – best are O(n log n) Some are slower – they’re always O(n 2 ) Some are O(n 2 ) in the worst case, but on average, they’re better than that. We’re going to try an insertion sort

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How an insertion sort works Consider the event at some position (1..n) Compare it to all the events before that position backwards—towards 0. If the comparison event time is LESS THAN the considered event time, then shift the comparison event down to make room. Wherever we stop, that’s where the considered event goes. Consider the next event…until done

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Insertion Sort public void sort(){ // Perform an insertion sort // For comparing to elements at smaller indices SimEvent considered = null; SimEvent compareEvent = null; // Just for use in loop // Smaller index we're comparing to int compare; // Start out assuming that position 0 is "sorted" // When position==1, compare elements at indices 0 and 1 // When position==2, compare at indices 0, 1, and 2, etc. for (int position=1; position < elements.size(); position++){ considered = (SimEvent) elements.get(position); // Now, we look at "considered" versus the elements // less than "compare" compare = position; // While the considered event is greater than the compared event, // it's in the wrong place, so move the elements up one. compareEvent = (SimEvent) elements.get(compare-1); while (compareEvent.getTime() > considered.getTime()) { elements.set(compare,elements.get(compar e-1)); compare = compare-1; // If we get to the end of the array, stop if (compare <= 0) {break;} // else get ready for the next time through the loop else {compareEvent = (SimEvent) elements.get(compare-1);} } // Wherever we stopped, this is where "considered" belongs elements.set(compare,considered); } // for all positions 1 to the end } // end of sort() Trace this out to convince yourself it works!

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Useful Links on Sorting http://ciips.ee.uwa.edu.au/~morris/Year2 /PLDS210/sorting.html http://ciips.ee.uwa.edu.au/~morris/Year2 /PLDS210/sorting.html http://www.cs.ubc.ca/spider/harrison/Jav a/sorting-demo.html http://www.cs.ubc.ca/spider/harrison/Jav a/sorting-demo.html http://www.cs.brockport.edu/cs/java/apps /sorters/insertsort.html http://www.cs.brockport.edu/cs/java/apps /sorters/insertsort.html These include animations that help to see how it’s all working Recommended

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Option #2: Put it in the right place /** * Add the event. * The Queue MUST remain in order, from lowest time to highest. **/ public void add(SimEvent myEvent){ // Option one: Add then sort //elements.add(myEvent); //this.sort(); //Option two: Insert into order this.insertInOrder(myEvent); }

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insertInOrder() /** * Put thisEvent into elements, assuming * that it's already in order. **/ public void insertInOrder(SimEvent thisEvent){ SimEvent comparison = null; // Have we inserted yet? boolean inserted = false; for (int i=0; i < elements.size(); i++){ comparison = (SimEvent) elements.get(i); // Assume elements from 0..i are less than thisEvent // If the element time is GREATER, insert here and // shift the rest down if (thisEvent.getTime() < comparison.getTime()) { //Insert it here inserted = true; elements.add(i,thisEvent); break; // We can stop the search loop } } // end for // Did we get through the list without finding something // greater? Must be greater than any currently there! if (!inserted) { // Insert it at the end elements.addLast(thisEvent);} } Again, trace it out to convince yourself that it works!

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Finally: A Discrete Event Simulation Now, we can assemble queues, different kinds of random, and a sorted EventQueue to create a discrete event simulation.

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What questions we can answer How long do distributors wait? Subtract the time that they unblock from the time that they block How much product sits in the warehouse? At each time a distributor leaves, figure out how much is left in the warehouse. How long does the line get at the warehouse? At each block, count the size of the queue. Can we move more product by having more distributors or more trucks? Try it!

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DESimulation: Sets the Stage DESimulation calls setUp to create agents and schedule the first events. It provides log for writing things out to the console and a text file. When it run()’s, it processes each event in the event queue and tells the corresponding agent to process a particular message.

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What a DESimulation does: // While we're not yet at the stop time, // and there are more events to process while ((now < stopTime) && (!events.empty())) { topEvent = events.pop(); // Whatever event is next, that time is now now = topEvent.getTime(); // Let the agent now that its event has occurred topAgent = topEvent.getAgent(); topAgent.processEvent(topEvent.getMessage()); // repaint the world to show the movement // IF there is a world if (world != null) { world.repaint();} // Do the end of step processing this.endStep((int) now); } As long as there are events in the queue, and we’re not at the stopTime: Grab an event. Make it’s time “now” Process the event.

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What’s an Event (SimEvent)? /** * SimulationEvent (SimEvent) -- an event that occurs in a simulation, * like a truck arriving at a factory, or a salesperson leaving the * market **/ public class SimEvent{ /// Fields /// /** When does this event occur? */ public double time; /** To whom does it occur? Who should be informed when it occurred? */ public DEAgent whom; /** What is the event? We'll use integers to represent the meaning * of the event -- the "message" of the event. * Each agent will know the meaning of the integer for themselves. **/ public int message; It’s a time, an Agent, and an integer that the Agent will understand as a message

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DEAgent: Process events, block if needed DEAgents define the constants for messages: What will be the main events for this agent? If the agent needs a resource, it asks to see if it’s available, and if not, it blocks itself. It will be told to unblock when it’s ready. Agents are responsible for scheduling their OWN next event!

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How Trucks start /** * Set up the truck * Start out at the factory **/ public void init(Simulation thisSim){ // Do the default init super.init(thisSim); this.setPenDown(false); // Pen up this.setBodyColor(Color.green); // Let green deliver! // Show the truck at the factory this.moveTo(30,350); // Load up at the factory, and set off for the warehouse load = this.newLoad(); ((DESimulation) thisSim).addEvent( new SimEvent(this,tripTime(),WAREHOUSE_ARRIVE)); } The truck gets a load, then schedules itself to arrive at the Warehouse.

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newLoad() uses uniform /** A new load is between 10 and 20 on a uniform distribution */ public int newLoad(){ return 10+randNumGen.nextInt(11); }

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How a Truck processes Events /** * Process an event. * Default is to do nothing with it. **/ public void processEvent(int message){ switch(message){ case FACTORY_ARRIVE: // Show the truck at the factory ((DESimulation) simulation).log(this.getName()+"\t Arrived at factory"); this.moveTo(30,350); // Load up at the factory, and set off for the warehouse load = this.newLoad(); ((DESimulation) simulation).addEvent( new SimEvent(this,tripTime(),WAREHOUSE_ARRIVE)); break;

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What Resources do They keep track of what amount they have available (of whatever the resource is). They keep a queue of agents that are blocked on this resource. They can add to the resource, or have it consume(d). When more resource comes in, the head of the queue gets asked if it’s enough. If so, it can unblock.

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How Resources alert agents /** * Add more produced resource. * Is there enough to unblock the first * Agent in the Queue? **/ public void add(int production) { amount = amount + production; if (!blocked.empty()){ // Ask the next Agent in the queue if it can be unblocked DEAgent topOne = (DEAgent) blocked.peek(); // Is it ready to run given this resource? if (topOne.isReady(this)) { // Remove it from the queue topOne = (DEAgent) blocked.pop(); // And tell it it’s unblocked topOne.unblocked(this); }

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Distributors start in the Market public void init(Simulation thisSim){ //First, do the normal stuff super.init(thisSim); this.setPenDown(false); // Pen up this.setBodyColor(Color.blue); // Go Blue! // Show the distributor in the market this.moveTo(600,460); // At far right // Get the orders, and set off for the warehouse amountOrdered = this.newOrders(); ((DESimulation) thisSim).addEvent( new SimEvent(this,tripTime(),WAREHOUSE_ARRIVE)); }

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Distributors have 3 events Arrive in Market: Schedule how long it’ll take to deliver. Leave Market: Schedule arrive at the Factory Arrive at Warehouse: Is there enough product available? If not, block and wait for trucks to bring enough product.

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Processing Distributor Events /** * Process an event. * Default is to do nothing with it. **/ public void processEvent(int message){ switch(message){ case MARKET_ARRIVE: // Show the distributor at the market, far left ((DESimulation) simulation).log(this.getName()+"\t Arrived at market"); this.moveTo(210,460); // Schedule time to deliver ((DESimulation) simulation).addEvent( new SimEvent(this,timeToDeliver(),MARKET_LEAVE)); break;

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Leaving the Market case MARKET_LEAVE: // Show the distributor at the market, far right ((DESimulation) simulation).log(this.getName()+"\t Leaving market"); this.moveTo(600,460); // Get the orders, and set off for the warehouse amountOrdered = this.newOrders(); ((DESimulation) simulation).addEvent( new SimEvent(this,tripTime(),WAREHOUSE_ARRIVE)); break;

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Arriving at the Warehouse case WAREHOUSE_ARRIVE: // Show the distributor at the warehouse ((DESimulation) simulation).log(this.getName()+"\t Arrived at warehouse"); this.moveTo(600,50); // Is there enough product available? Resource warehouseProduct = ((FactorySimulation) simulation).getProduct(); if (warehouseProduct.amountAvailable() >= amountOrdered) { // Consume the resource for the orders warehouseProduct.consume(amountOrdered); // Zero time to load? ((DESimulation) simulation).log(this.getName()+"\t Gathered product for orders of \t"+amountOrdered); // Schedule myself to arrive at the Market ((DESimulation) simulation).addEvent( new SimEvent(this,tripTime(),MARKET_ARRIVE)); } else {// We have to wait until more product arrives! ((DESimulation) simulation).log(this.getName()+"\t is blocking"); waitFor(((FactorySimulation) simulation).getProduct());} break;

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Is there enough product? /** Are we ready to be unlocked? */ public boolean isReady(Resource res) { // Is the amount in the factory more than our orders? return ((FactorySimulation) simulation).getProduct().amountAvailable() >= amountOrdered;}

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The Master Data Structure List: We use almost everything here! Queues: For storing the agents waiting in line. EventQueues: For storing the events scheduled to occur. LinkedList: For storing all the agents.